QuestionConsider the graph shown. a. Select the best possible wording for the situation depicted in the given graph: Ida sells 5 boxes of cookies to family members, and for every door she knocks on in her neighborhood, she sells another 1 boxes of cookies. Ida sells 6 boxes of cookies for every door in her neighborhood that she knocks on. Ida's own family bought 1 boxes of cookies, and for every door in her neighborhood Ida knocks on to sell cookies, she sells 5 additional boxes of cookies. Ida sold \ $1 of cookies to family members, and for every door in her neighborhood she knocks on, she makes another \$5 selling cookies. b. How do we know, based on the given graph, that the relation between the number of doors Ida knocks on, and the number of boxes of cookies she sells, is a linear function? Because the graph is a straight line (or contains points that are arranged in a straight line) and passes the vertical line test. It's impossible to tell from looking at the graph that it represents a linear function. Because on the graph, the$ y-values increase from left to right. Because the graph has units labeled on both axes. c. Fill in the given table with the correct missing values. \begin{tabular}{|c|c|} \hlinex (number of doors Ida knocks on) & y (total number fo boxes of cookies Ida sells) \\ \hline 0 & \square \\ \hline 1 & \square \\ \hline 5 & \\ \hline\square \\ \hline \end{tabular} d. Write the linear function relating the number of doors Ida knocks on, x $, to the total number of boxes of cookies she sells,$ y . y=\square$

Studdy Solution

STEP 1

1. The graph is a straight line, indicating a linear relationship.
2. The line passes through the points (0, 1) and (5, 6).
3. The x-axis represents the number of doors Ida knocks on, and the y-axis represents the total number of boxes of cookies Ida sells.

STEP 2

1. Interpret the wording options based on the graph.
2. Determine why the relationship is linear.
3. Fill in the missing values in the table.
4. Write the linear function.

STEP 3

The graph shows that when Ida knocks on 0 doors, she sells 1 box of cookies, and for every additional door, she sells 1 more box. This matches the wording: "Ida's own family bought 1 boxes of cookies, and for every door in her neighborhood Ida knocks on to sell cookies, she sells 5 additional boxes of cookies."

STEP 4

The graph is a straight line, which indicates a linear relationship. This is confirmed by the fact that it passes the vertical line test, meaning each x-value corresponds to exactly one y-value.

STEP 5

Using the points (0, 1) and (5, 6), we can determine the missing values in the table.
- At $x = 0$ , $y = 1$ . - At $x = 1$ , the line increases by 1 for each additional door, so $y = 2$ . - At $x = 5$ , $y = 6$ .
The missing value for $x = 5$ is already given as 6.

STEP 6

To find the linear function, we use the slope-intercept form $y = mx + b$ .
- The slope $m$ is calculated as $\frac{6 - 1}{5 - 0} = 1$ . - The y-intercept $b$ is the value of $y$ when $x = 0$ , which is 1.
Thus, the linear function is $y = 1x + 1$ or simply $y = x + 1$ .
The linear function is:
$y = x + 1$

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